2018/11/05 by Mark Shoemaker, Shoemaker, Mark
Mathematics · #14E16 #14N35 #53D45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1811.01888
openalex publication_date 2018/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given Y a non-compact manifold or orbifold, we define a natural subspace of the cohomology of Y called the narrow cohomology. We show that despite Y being non-compact, there is a well-defined and non-degenerate pairing on this subspace. The narrow cohomology proves useful for the study of genus zero Gromov-Witten theory. When Y is a smooth complex variety or Deligne-Mumford stack, one can define a quantum D-module on the narrow cohomology of Y. This yields a new formulation of quantum Serre duality.